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1.5: Dividing Fractions

  • Page ID
    7085
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    When dividing fractions you invert (flip upside down) the fraction on the right side of the equation (the dividend). Then it becomes a multiplication problem. Invert and multiply!

    Example \(\PageIndex{1}\)

    \(\dfrac{2}{5} \div \dfrac{1}{2} \rightarrow \dfrac{2}{5} \times \dfrac{2}{1}=\dfrac{4}{5}\)

    Example \(\PageIndex{2}\)

    \(\dfrac {\dfrac{4}{9}}{\dfrac{8}{9}}\)

    This example reads \(\dfrac{4}{9}\) divided by \(\dfrac{8}{9}\).

    However, after you “invert and multiply,” it becomes:

    \[\dfrac{4}{9} \times \dfrac{9}{8} \rightarrow \dfrac{1}{1} \times \dfrac{1}{2}=\dfrac{1}{2} \nonumber \]

    After inverting the fraction, the same rules apply as previously mentioned when multiplying fractions. You need to change mixed numbers into improper fractions; you can cross cancel, and always remember to reduce if necessary.

    Example \(\PageIndex{3}\)

    \(\dfrac{3}{8} \div \dfrac{12}{6} \rightarrow \dfrac{3}{8} \times \dfrac{6}{12} \rightarrow \dfrac{\not{3}}{\not {8}} \times \dfrac{\not {6}}{\not {12}}=\dfrac{1}{4} \times \dfrac{3}{4}=\dfrac{3}{16}\)

    In the Example \(\PageIndex{3}\) above the 3 divided into itself once and into the 12 four times. Similarly, 2 divided into 6, three times and into 8, four times. Can you see a different way to cross cancel?

    If the dividend is a whole number write it as a fraction before inverting. Always remember to cross cancel and reduce if necessary.

    Example \(\PageIndex{4}\)

    \(\dfrac{5}{8} \div 10 \rightarrow \dfrac{5}{8} \div \dfrac{10}{1} \rightarrow \dfrac{5}{8} \times \dfrac{1}{10} \rightarrow \dfrac{\not{5}}{8} \times \dfrac{1}{\not {10}} \rightarrow \dfrac{1}{8} \times \dfrac{1}{2}=\dfrac{1}{16}\)

    Exercise 1.5

    Divide the following and reduce if necessary.

    1. \(\dfrac{1}{2} \div \dfrac{2}{4}\)
    2. \(\dfrac{5}{22} \div 7 \dfrac{2}{4}\)
    3. \(\dfrac{6}{8} \div \dfrac{9}{12}\)
    4. \(3 \dfrac{1}{3} \div 10\)
    5. \(5 \dfrac{1}{4} \div 8 \dfrac{1}{2}\)
    6. \(\dfrac{8}{16} \div \dfrac{16}{8}\)
    7. \(4 \div 3 \dfrac{2}{3}\)
    8. \(\dfrac{2}{5} \div 5 \dfrac{6}{9}\)
    9. \(\dfrac{9}{13} \div 9\)
    10. \(\dfrac{11}{22} \div \dfrac{1}{2}\)
    11. \(2 \dfrac{9}{20} \div 5 \dfrac{2}{5}\)
    12. \(3 \dfrac{1}{2} \div 9 \dfrac{1}{2}\)
    13. \(5 \div 25\)
    14. \(\dfrac{10}{3} \div \dfrac{1}{6}\)
    15. \(\dfrac{13}{33} \div \dfrac{39}{3}\)
    16. \(100 \dfrac{1}{2} \div 10 \dfrac{5}{6}\)

    1.5: Dividing Fractions is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.

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